In the above equations the following parameters are defined:
\(t^{\prime \prime }(k_x) = 2 \lambda _{\text{SO}} \sin (\frac{k_x}{2})\) , \(t^\prime (k_x) = 2 t \cos (\frac{k_x}{2})\) , and
\(\Delta (k_x)=2\lambda _{\text{SO}} \sin (k_x)\) .
Here we should emphasize that we considered the unit cell length to be \(a\)  = 1 and used the gauge transformation [1]} \(c_{k_x,m} \rightarrow e^{i\frac{k_x}{2}} c_{k_x,m}\)  only on the sites located on the right side of the unit cell (with index \(m=2,3,6,7,\dots \) ) to get rid of the factor \(e^{i\frac{k_x}{2}}\)  in hopping amplitudes \(t^{\prime }\)  and \(t^{\prime \prime }\)  as well.
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